الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
In the present thesis, the shear behaviour of RC beams under blast loading is studied numerically by the nonlinear FE program ABAQUS / Explicit. Nonlinear stress-strain relations are used for concrete and reinforcing steel to simulate the material behaviour in compression and. To get a reasonable estimation of induced damage. In the geometry of idealization of R.C beams, rather small element size are used in all analyses. the time increment size was selected to satisfy the numerical stability condition of the nonlinear dynamic analysis. The strain rate effect is included on the concrete and steel material properties. The proposed numerical model and constitutive laws are successfully used to predict the experimental response of several RC beams; tested in the literature.
Comprehensive parametric studies were performed and presented in the thesis to study the different shear response characteristics of RC beams with different concrete compressive strength, steel yield stress, longitudinal and web reinforcement ratios. The parametric studies were done using program ABAQUS / Explicit. The research objectives were to study effect of the test variables on the structural response characteristics of RC beams which include the following: shear carrying capacity, load deflection curves, and cracking patterns.
SDOF method was used as a simple analysis and design tool for the dynamic shear strength of RC beams. This approach is designed for the distributed loaded simply supported RC beams with empirical modifications. The proposed SDOF system accounts for the effects of concrete compressive and tensile strengths, shear span to depth ratio, longitudinal reinforcement ratio, and displacement ductility ratio. The analytical predicted results of shear strength for forty three R.C beams are in a good agreement with the experimental results.
7.2 Conclusive Points of F.E Validation and Parametric Studies
from the verification and parametric studies in the present work, the following conclusions are drawn for RC beams in shear under blast loading:
1. The ABAQUS / Explicit geometrical model combined with the proposed constitutive models for concrete in compression and tension is validated to predict the behaviour of concrete beams with different shapes under dynamic load. The nonlinear response of RC beams is successfully predicted for different displacement ductility levels and blast loading cases.
2. For blast-loaded R.C beams, the maximum shear force increases with the increase of load value and duration. The end reaction increases by 22% due to 33% pressure increase and by 9% due to 67% duration increase. The mid-span deflection increases with the increase of pressure value or load duration, the maximum displacement increases by 64% due to 33% pressure increase and by 21% due to 67% duration increase. The time rise of blast pressure has a small effect on displacement and shear response.
3. There is a slight decrease in the maximum shear force for blast loaded beams with the increase of concrete compressive strength, longitudinal steel yield stress and stirrups yield stress. It’s estimated to be 13.5% decrease due to 36.4% concrete strength increase, 12% decrease due to 52% yield stress increase of main steel, and 8.5% decrease due to 67% stirrups yield stress increase. The central deflection decreases with increase the concrete strength and longitudinal steel yield stress. The maximum displacement decreases by 23.1% due to 36.4% concrete strength increase and by 16% due to 108% increase of longitudinal steel yield stress. The central displacement is not affected by the increase of stirrups yield stress.
4. The maximum shear force in blast-loaded R.C beams decreases slightly with the increase of main steel ratio and stirrups ratio. The end reaction decreases by 6% due to 80% increase of main steel ratio and by 17% due to 100% stirrups ratio increase. The mid-span displacement significantly decreases with the increase of main and secondary steel ratios. The deflection decreases by 35% due to 80% increase of main steel ratio and by 23% due to 55% increase of secondary steel ratio. The mid span deflection decreases by 8% with 100% increase of stirrups ratio.
5. The mid-span deflection shape is almost the same with different mesh size. While, the maximum shear force increases by 11.1% with the 50% decrease of mesh size. The strain rate effect decreases the mid span deflection by 48%.While the shear force decreases by 9.1%. The inclusion of damage parameters increases the mid span deflection by 10.5%, and decreases the support reaction by 17.5%.
7.3 Conclusive Points of SDOF Studies
from the results of the validation and comparative studies of the proposed SDOF method for shear strength model for RC beams, the following conclusions are presented:
1. The proposed SDOF method is successful in predicting the end shear reaction of 43 uniformly loaded simply supported R.C beams with different material, geometrical, loading, and modelling parameters. The overall average ratio between the experimental shear strength to the predicted strength is of value 1.29 for all tested beams with accuracy of this method about 87.7%.
2. The shear capacity increases with the increase of the concrete strength. The rate of shear increase decreases with the increase of load duration ratio (td / TN). The ratio between dynamic to static shear capacity is 1.4 at load duration ratio = 1.15, and is 1.13 at load duration ratio = 2.85 [1].
3. The shear capacity increases with the increase of yield stress of longitudinal steel due to the enhancement of moment capacity of the beam. The ratio of dynamic to static shear capacity is 2.33 at load duration ratio = 1.15 and is 1.13 at load duration ratio = 2.85.
4. In general, the applied shear force increases with the increase of applied load amplitude. The ratio of dynamic to static shear capacity is 1.5 at load duration ratio = 1.15 and is 0.8 at load duration ratio = 2.85.
7.4 Recommendations for Future Studies
For improving the prediction of the behaviour of RC beams in shear and flexure, the present theoretical research works can be extended to study the following parameters:
1. The effect of geometrical and structural systems such as:
i. Continues and fixed beams.
ii. Beams with variable inertia.
iii. Framed beam-column systems.
2. The effect of other concrete material types such as:
i. High strength concrete;
ii. Steel fiber RC;
iii. Polymer modified concrete.
3. The effect of other loading types such as:
i. Fatigue loading;
ii. Torsional loading;
iii. Cyclic loading;
iv. Ground motion loading.
4. Improving the numerical modelling of RC elements under blast loading by:
i. Bond-Slip model for the interaction between concrete and steel.
ii. Discrete crack approach for the representation of crack propagation